Different subject matter for a wide range of topics are analyzed and measured using various empirical studies and experimental tests that produce test results, which form distribution patterns when combined with the scales, metrics, and measures that were used. There are many well-known discrete distribution patterns such as Weibull, Bernoulli, binomial, negative binomial, Poisson and geometric distributions. There are many well-known continuous distributions such as uniform, normal, exponential, gamma and beta distributions.
A distribution pattern for an object is created by graphing variations in a characteristic of the object. For example, an x-axis can represent the mass of each object, and a y-axis can represent the number of the objects with a given mass. Statistically, the resulting distribution pattern for the object is typically a bell curve where the objects with the most common mass peak at the top of the bell.
Various types of scales are used to measure subject matter, including nominal, ordinal, interval and ratio scales. Scales, such as a numerical scale which simply counts objects, a scale such as meters to measure distance, a scale such as seconds to measure time, a scale such as bit rate to measure data transmission, a scale such as the Richter scale to measure earthquakes, etc. Metrics are measures of key attributes that often yield information about observed phenomena. Metrics provide a basis for empirical validation of theories and relationships between concepts. There are different metrics for different subjects that are meaningful and widely accepted, such as gas-mileage for an automobile or bit rate for a network, and should be re-used for subsequent analysis and comparison of objects within these subjects.
Statistics is the study of the collection, organization, analysis, interpretation, and presentation of data. The mathematical functions used in statistics provide a means to analyze data and add meaning to the measurements. Statistics can also be used for the planning of data collection in terms of the design of surveys and experiments. Statisticians can improve data quality by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting the use of data and statistical models.
In addition, data patterns may be modeled in a way that account for randomness and uncertainty in the observations. These models can be used to draw inferences about the process or population under study; a practice called inferential statistics. Inference is a vital element of scientific advance, since it provides a way to draw conclusions from data that are subject to random variation. To prove the propositions being investigated further, the conclusions are tested as well, as part of the scientific method. Descriptive statistics and analysis of the new data tend to provide more information as to the truth of the proposition. Statistics is closely related to probability theory, with which it is often grouped. The difference is, roughly, that probability theory starts from the given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction by inductively inferring from samples to the parameters of a larger or total population.
Probability theory is the branch of mathematics concerned with probability, the analysis of seemingly random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
The application of probability and statistics to analyze a data set can provide valuable insight into observed phenomena. Knowledge of which approach to use when gathering data, which mathematical function to apply to the data set, or which distribution pattern best encompasses the data is not always clear. Known solutions to this problem require in-depth knowledge by an individual, who can then make a determination as to which approach, mathematical function, or distribution pattern to use. However, there are currently a large number of possible approaches, mathematical functions, and distribution patterns to choose from and the number of options are continually increasing. As such, the detailed knowledge required to identify an appropriate measure, metric, or distribution pattern for a given type of test or type of data is also increasing. If a person knows what type of distribution pattern to expect for test results, the person will know if test results obtained by the person are reasonable and indicate that the test conducted by the person was valid.
An object of the invention is to assist a person in determining a distribution pattern to expect for a test or metric.